Effective mechanical properties of auxetic materials: Numerical predictions using variational asymptotic method based homogenization

In this work, the variational asymptotic method (VAM) based homogenization framework is used for the first time to determine the equivalent elastic stiffness tensor of auxetic materials. The proposed method allows the structural elements of the auxetic unit cell to naturally incorporate rotational degrees of freedom, without any ad-hoc assumptions. The overall macroscale homogenized response of the unit-cells is considered to be fully anisotropic; specific possible responses, representative of orthotropy or transverse isotropy naturally emerge from the VAM-based homogenization, due to the arrangements of the structural elements making up the unit-cell. For all the auxetic unit cell geometries considered in this study, the predictions obtained from the in-house python-based implementation of the VAM-based homogenization framework are validated using commercial finite element software (Abaqus) and open literature. The results demonstrate the versatility and the computational efficiency of the VAM-based homogenization framework to describe auxetic metamaterials.